I think Siggy could actually work! It's short and spunky and very straightforward. I think it's actually pretty fashionable sounding. Siggy is also my favorite spelling. As for similar names I think...

I think Lucky for Lachlan would be quite cute, but I have to say, is your son naming him? You should be able to use the name regardless of what he wants the nickname to be. As far as other nicknames...